Field of the Invention
The present invention generally relates to computer software. More specifically, the present invention relates to techniques for decomposing three-dimensional (3D) geometry into developable surface patches and two-dimensional (2D) cut patterns.
Description of the Related Art
A number of sheet materials used to manufacture objects strongly resist stretching and shearing, but not bending. Such materials include sheet metal, textiles, and sheets of wood, each of which is typically easy to mass-produce and cut into shapes using, e.g., stamping, water jet, or laser cutters. Use of such materials may be cost-effective and preferable to more expensive molded or machined parts. However, each part, once cut to shape, can only be (approximately) isometrically deformed, as the properties of the materials allow bending, but not in-plane stretching or shearing in the final configuration. It is easily verifiable that the class of shapes such parts are deformable into is a subclass of “developable” surfaces, i.e., surfaces with zero Gaussian curvature, or equivalently, those surfaces that have only one (and perhaps no) non-zero principal curvature at each point. Examples of such developable surfaces include a plane and a cone, whereas a sphere is an example of a non-developable surface.
Given a 3D shape that is to be produced using the sheet materials just discussed, it is desirable to identify patches on the surface of the 3D shape that are developable, or approximately developable, so that the patches may be built using an appropriately shaped piece of the sheet material.